According to the prior art, there are several types of modulation for multi-carrier signals, such as DMT (Discrete MultiTone) modulation or OFDM (Orthogonal Frequency Division Multiplexing) modulation or COFDM (corresponding to a coded OFDM modulation). According to the prior art, the demodulation of a multi-carrier signal implements an FFT (Fast Fourier Transform) based on a binary representation of an OFDM symbol. Hence, the document entitled “Principles of modulation and channel coding for digital broadcasting for mobile receivers” (by Alard and Lassale and published in August 1987 in the EBU technical revue) describes a method for the demodulation of an ODFM signal implementing an FFT. COFDM modulation is also implemented in numerous radio telecommunications standards particularly for DAB (Digital Audio Broadcasting), DVB-T (Digital Video Broadcasting—Terrestrial), DVB-H (DVB-Handheld), IEEE 802.11 to 5 GHz, IEEE 802.16.
An FFT at N points (for example 256) involves taking N complex inputs (the ith input being noted input(i)) and supplying N outputs (the kth output being noted output(k)) as defined hereafter:
                              Output          ⁡                      (            k            )                          =                              ∑                          i              =                                                                    -                    N                                    /                  2                                +                1                                                    N              /              2                                ⁢                                    input              ⁡                              (                i                )                                      *                          exp              ⁡                              (                                                      -                    2                                    ⁢                  j                  ⁢                                                                          ⁢                  i                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                                      k                    /                    N                                                  )                                                                        (        1        )            
The k integer being comprised in the interval ]−N/2;+N/2] and where j corresponds to a purely imaginary number.
According to the formula (1), the number of multiplications and additions is of the order of N2. According to the prior art, in order to reduce the number of operations, an elementary operation is used called the butterfly. This operation is in multiple steps and of a complexity of the order of N*Log(N) operations, where the operator Log is expressed in the “radix” base and is typically equal to 2 or 4. Hence, an FFT at 64 points is typically in three steps in a base of 4 or in six steps in a base of 2 (64=42=26). At each step, the input signal is multiplied on n bits by a “twiddle” factor on p bits. The result of a step is rounded off prior to being used as an input for the following step, the multiplier being particularly large (for example 12×10 bits). Typically, an FFT module waits for the last block sample to come and can deliver an FFT output a few clock cycles later.
Hence, the prior art presents the inconvenience of being relatively complex especially when the number of carriers is low.